Molecular Ecology (2006) 15, 209–223
doi: 10.1111/j.1365-294X.2005.02718.x
Comparative phylogeographic summary statistics for testing
simultaneous vicariance
Blackwell Publishing, Ltd.
M . J . H I C K E R S O N ,* G . D O L M A N † and C . M O R I T Z *
*Museum of Vertebrate Zoology, University of California, 3101 Valley Life Sciences Building, Berkeley, California 94720-3160, USA,
†Department of Zoology and Entomology, University of Queensland, St Lucia, 4072, Australia
Abstract
Testing for simultaneous vicariance across comparative phylogeographic data sets is
a notoriously difficult problem hindered by mutational variance, the coalescent variance,
and variability across pairs of sister taxa in parameters that affect genetic divergence.
We simulate vicariance to characterize the behaviour of several commonly used summary
statistics across a range of divergence times, and to characterize this behaviour in comparative phylogeographic datasets having multiple taxon-pairs. We found Tajima’s D to be
relatively uncorrelated with other summary statistics across divergence times, and
using simple hypothesis testing of simultaneous vicariance given variable population
sizes, we counter-intuitively found that the variance across taxon pairs in Nei and Li’s net
πnet), a common measure of population divergence, is often inferior
nucleotide divergence (π
to using the variance in Tajima’s D across taxon pairs as a test statistic to distinguish
ancient simultaneous vicariance from variable vicariance histories. The opposite and more
intuitive pattern is found for testing more recent simultaneous vicariance, and overall we
found that depending on the timing of vicariance, one of these two test statistics can achieve
high statistical power for rejecting simultaneous vicariance, given a reasonable number of
intron loci (> 5 loci, 400 bp) and a range of conditions. These results suggest that components of these two composite summary statistics should be used in future simulation-based
methods which can simultaneously use a pool of summary statistics to test comparative the
phylogeographic hypotheses we consider here.
Keywords: coalescent, comparative phylogeography, simultaneous vicariance, statistical power,
summary statistic
Received 20 March 2005; revision received 24 June 2005; accepted 25 July 2005
Introduction
One of the most central yet challenging puzzles in biogeography is whether codistributed taxon pairs share a common
history of simultaneous vicariance (Darwin 1859; Nelson
& Platnick 1981; Ricklefs & Schluter 1993; Avise et al. 1998;
Johns & Avise 1998; Knowlton & Weigt 1998; Schneider
et al. 1998; Riddle et al. 2000; Johnson & Cicero 2004). While
conceptually simple, testing for simultaneous divergence
with genetic data is obscured by differences among taxon
pairs in parameters that affect genetic divergence including
mutation rates, ancestral population sizes, postdivergence
migration (admixture), and ancestral subdivision. Even when
Correspondence: Michael J. Hickerson, Fax: (510) 643 - 8238;
E-mail: [email protected]
© 2006 Blackwell Publishing Ltd
there is equality in such parameters across taxon pairs,
substantial variation in genetic divergence will arise from
mutational and coalescent variance, especially in taxa that
are heavily subdivided or have large and stable effective
population sizes (Arbogast et al. 2002; Hickerson et al. 2003).
In addition to these difficulties, incorrect sister species status
from undetected extinction events can also hinder inference
(Johnson & Cicero 2004).
Maximum-likelihood and Bayesian methods can in
principle tease apart simultaneous and variable divergence
histories by utilizing the full information content from the
data (Bahlo & Griffiths 2000; Edwards & Beerli 2000; Nielsen
& Wakeley 2001). However, extending these methods to
simultaneously analyse multiple phylogeographic data sets
involving complex models and idiosyncratic biogeographic
histories is less tractable than simulation-based methods
210 M . J . H I C K E R S O N , G . D O L M A N and C . M O R I T Z
such as approximate likelihood and approximate Bayesian
computation (ABC). Although such simulation-based approximate methods utilize less information from the data using
summary statistics, they allow greater flexibility and can
better handle complicated and highly parameterized models
because the likelihood function, P(data|Φ) does not have
to be calculated explicitly. Furthermore, simulation-based
methods can easily incorporate a priori idiosyncratic
biological realism or uncertainty in nuisance parameters
(Pritchard et al. 1999; Estoup et al. 2001; Beaumont et al. 2002;
Beaumont 2004). Such methods have been developed for
testing demographic histories of a single taxon (Tavaré
et al. 1997; Weiss & von Haeseler 1998; Estoup et al. 2004;
Tallmon et al. 2004; Excoffier et al. 2005) and phylogenetic
questions (Plagnol & Tavare 2002), but histories involving
sets of geographically codistributed taxa have not yet been
considered.
However, such simulation-based approximate methods
work best when using summary statistics that are relatively
unbiased and contain relevant information regarding a
parameter that is to be estimated, such as using the average
number of pairwise differences between individuals to
estimate θ (4 * the effective population size * mutation
rate) under neutrality and panmixia (Tajima 1983). When
testing more complex hypotheses such as estimating the
distribution of divergence times across taxon pairs, a single
summary statistic might not contain enough information
for robust inference across parameter space. In such cases,
a simulation-based method would benefit from simultaneously using a set of summary statistics that together capture
the essential features in the data.
Therefore, before embarking on a full ABC or approximate likelihood method for comparative phylogeographic
parameter estimation and hypothesis testing, we must
identify a pool of minimally correlated summary statistics
that independently demonstrate some statistical power
regarding comparative phylogeographic hypothesis testing. To this end we employ simulations to investigate the
behaviour of various summary statistics under various single
and multiple taxon-pair vicariance models. Specifically, we
use simulations to investigate: (i) the general properties of
several commonly used summary statistics (Table 1) including
Table 1 Summary statistics of single taxon-pair divergence histories. The proposed comparative phylogeographic summary statistics
involve calculating variance of a subset of these summary statistics across 10 taxon pairs or covariance of pairs of a subset of these summary
statistics. All summary statistics are averaged across loci within each taxon pair
(a)
Notation
Summary statistic
Reference
Expectation and variance
derived under vicariance
π
Average pairwise differences
Tajima 1983
Yes


 n
πij 

 2 ; πij = differences


 
i< j


between the ith and jth sequence;
n is the number of DNA sequences
sampled
πb
Average pairwise differences
between populations
Takahata &
Nei 1985
Yes
π restricted to between population
comparisons
πw
Average pairwise differences
within populations
Takahata &
Nei 1985
Yes
π restricted to within population
comparisons
πnet
Net average pairwise
differences between
populations
Takahata
& Nei 1985
Yes
πb − πw
S
Raw number of segregating
sites
Watterson
1975
Expectation: Wakeley & Hey 1997
Variance under extreme vicariance:
Hudson, Kreitman & Aguadé 1987
Number of Polymorphic sites
θW
Watterson’s theta (number of
segregating sites normalized
for sample size)
Watterson
1975
No
D
Tajima’s D
Tajima 1989
No
Formula and/or description
∑∑
 n−1 
1
 ; n is number of DNA
S 
 i=1 i 


sequences sampled
∑
n−1 

1

D = π − S
e1S + e2S(S − 1);
i

i=1 

e1 and e2 are coefficients defined in Tajima
(1989) n is number of DNA sequences
sampled
∑
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
P H Y L O G E O G R A P H I C S U M M A R Y S T A T I S T I C S 211
Fig. 1 A depiction of the model involving one ancestral population splitting into two-daughter populations at time τ (4N generations)
before the present. The population mutation parameters are θA, θ1,
and θ2, where each θ is 4 * N * µ, such that µ is the per-gene pergeneration DNA mutation rate and where NA, N1, and N2 are effective
population sizes of the ancestral, and two-daughter populations,
respectively. Under the demographic expansion model, the twodaughter populations are of sizes NBott1 and NBott2, respectively,
for times τBott1 and τBott2, respectively.
their expectations, variances, and pairwise correlations
throughout a range of divergence times; (ii) the variances
and covariances across taxon pairs in a subset of these
summary statistics ( Table 1) under various simultaneous
and multiple vicariance histories (Figs 1 and 2); and (iii)
how statistical power to reject simultaneous vicariance
improves with collecting more nuclear loci under a simple
hypothesis testing framework in which the variance of a
summary statistic across taxon pairs or covariance of pairs
of summary statistics across taxon pairs are independently
used as test statistics (Excoffier et al. 2000; Knowles &
Maddison 2002; Hickerson & Cunningham 2005).
Results of this study will not only have general relevance
to comparative phylogeographic studies, but will additionally suggest a useful pool of summary statistics to use in
the full ABC framework we are concurrently developing
for comparative phylogeographic studies (Beaumont et al.
2002).
Materials and methods
This study is partially motivated by the comparative phylogeographic data set that is emerging from the Australian
Wet Tropics (AWT) in which multiple intron loci are being
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
Fig. 2 Density curves depicting prior distributions that define the
10 different multiple taxon-pair vicariance hypotheses. Under
each hypothesis, divergence time varies among taxon-pairs within
a data set by randomly drawing from each respective prior
distribution. The density curves in (a) and (b) are simulated from
a gamma distribution using different means and variances for τ.
The density curve depicting Huniform in (c) is a uniform distribution
with values of τ ranging between 0 and 5.5 million years. The
density curve depicting Hmixed in (c) is a mixture of gamma
distributions H0.025A, H0.25A, H2.5A, and H5.0A with equal probability. Divergence time is alternatively given in units of 4N generations
and years.
212 M . J . H I C K E R S O N , G . D O L M A N and C . M O R I T Z
Fig. 3 Density curve depicting the prior distribution defining
among-taxon-pair variation in θ (4Nµ) used in the 10 taxon-pair
vicariance simulations.
collected across taxon pairs that are codistributed across a
putative historical barrier to gene flow (the Black Mountain
barrier, Schneider et al. 1998). Therefore, we incorporate a
priori information on effective population sizes (Fig. 3),
mutation rates, generation times and divergence times that
are based on estimates from seven introns collected from
two carlia skink taxon pairs (Dolman & Phillips 2004; Dolman
& Moritz in review). The simulated single taxon-pair data
sets consisted of samples of 12 diploid individuals per sister
taxon and 400 bp introns per locus (Fig. 1). The simulated
comparative phylogeographic data sets were identical to
this, yet consisted of 10 taxon pairs per data set.
Summary statistics
We chose to explore summary statistics based on whether
they were likely to contain information relevant to the parameters in our model, such as effective population sizes,
divergence times, and other demographic processes (Table 1).
With this in mind we initially chose two compound
summary statistics (πnet and Tajima’s D) as well as their
components (πw and πb from the former and S, π, and θW
from the latter). Although Tajima’s D, S, π, and θW are
usually quantities that are calculated from a single species
or population, here we calculate each of these summary
statistics once per taxon pair as if they were being collected
from a single population or species. On the other hand, πnet
and its components (πw and πb) are calculated with each
sister taxon treated as a distinct population, such that πb is
the average pairwise differences between a sister pair, πw
is the average pairwise differences within the two sister taxa,
and πnet = πb – πw (Table 1). With respect to divergence
time, it is known that πb, πnet, Tajima’s D, S, π, θW all increase
as divergence time increases (Takahata & Nei 1985;
Hudson et al. 1987; Tajima 1989; Simonsen et al. 1995). With
respect to population sizes, we can expect πw, S, π, and θW
to all contain information (Watterson 1975; Tajima 1983;
Fu 1995; Vasco et al. 2001), and we should expect Tajima’s
D to extract information regarding population expansion
(Simonsen et al. 1995).
There were some commonly used summary statistics
that we did not consider because they are known to contain
less information for our parameters of interest. For example,
we considered πnet instead of FST, a commonly used metric
in population genetic studies. Although these two metrics
are very similar in that they both measure the ratio of interpopulation and intrapopulation genetic variance, we initially
chose the former because it is not upwardly bounded with
greater divergence times, while the latter has a maximum
value of 1.0. Likewise we did not choose to explore haplotype
diversity, the number of haplotypes or the number of singletons, because these measures do not have strong bearing
on divergence times. We also did not explore Fu and Li’s D
or F statistic because these measures are known to behave
very similar to Tajima’s D (Fu & Li 1993), but are only more
powerful than Tajima’s D when an outgroup is known
(Simonsen et al. 1995), a condition we do not assume.
Expectation, variance and correlation of summary
statistics
To select candidate summary statistics from our initial pool
(Table 1), we determined their mean and variance throughout a range of divergence times and determined the correlations between all pairs of these seven summary statistics
under the various divergence times. The three criteria for
selecting candidate summary statistics for use in the multiple
taxon-pair analyses were: (i) a strong linear relationship
between divergence time and the mean of the summary
statistic; (ii) low variance of the summary statistic; and (iii)
low correlation between a summary statistic and other
summary statistics satisfying 1 and 2 (through a range of τ).
When a pair of summary statistics was shown to be heavily
correlated, elimination was based on the degree to which
criteria 1 and 2 were satisfied by either summary statistic
and whether either of the two summary statistics were
correlated with other summary statistics.
The mean and variance of the seven summary statistics
(Table 1) were calculated from 100 000 single taxon-pair
data sets simulated under 10 divergence times discretely
ranging from 0.0 to 2.0 coalescent time units (i.e. zero to
approximately 5 million years ago (Ma) when scaled by
4N generations, generation time of 3 years and θ = 1.0). The
3-year generation time was taken from the two previously
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
P H Y L O G E O G R A P H I C S U M M A R Y S T A T I S T I C S 213
Table 2 Parameters used for simulation of vicariance histories depicted in Fig. 1
Parameter
Description
Values under single taxonpair vicariance histories
Prior distributions under 10 taxon-pair vicariance
histories
τ
Divergence time before the
present in units of 4N
generations
9 fixed values discretely
ranging between 0.0–2.0
(4N generations)
Gamma distributed under 11 different
hypotheses defined by various values of E(τ) and var(τ)
shown in Fig. 2a, b. Uniformly distributed under one
hypothesis with τ between 0.0 and 5.0 4N generations
(Fig. 2c), and a mixed gamma distribution under one
hypothesis with four means (Fig. 2c)
θ (4 * N * µ)
4 * effective population size
* DNA mutation rate with
α = 3.50 and β = 0.288 (Fig. 3)
1.0
Gamma distributed priors (per locus per generation);
NA = N1 = N2 where N1 and N2 correspond to daughter
taxon 1 and 2, respectively, and NA corresponds to the
ancestral population (Fig. 1)
NBott1 and NBott2
Effective population size of
daughter taxa 1 and 2 during
bottleneck (Fig. 1)
No bottleneck or fixed at
0.5N1 and 0.5N2
No bottleneck or fixed at 0.5N1 and 0.5N2
τBott1 and τBott2
Longevity of bottleneck
subsequent to τ in daughter
taxon 1 and 2
No bottleneck or fixed at 0.5τ
No bottleneck or fixed at 0.5τ
mentioned skink taxon pairs (Dolman & Moritz in review).
The population mutation parameter, θ (4Νµ), was fixed at
1.0, such that µ, the mutation rate was 1.2 × 10−6 per locus
per generation following an infinite sites model. Simulations
were conducted under a model without demographic
expansion and a model that included a bottleneck after
divergence such that the demographic expansion parameters
were NBott1 = 0.5N1, NBott2 = 0.5N1, τBott1 = 0.5τ, and τBott2 = 0.5τ
(Fig. 1; Table 2).
Although it is preferable to derive the expectation and
variance of these summary statistics rather than use
simulations, the range of models and summary statistics
we explore makes this endeavour beyond the scope of
this study. In cases where the first two moments have been
previously derived under vicariance models, we compare
the simulated expectations and variances to the derived
values as a check.
Multiple taxon-pair divergence model
For the multiple taxon-pair simulations, we implement
a hierarchy of parameters. The ‘higher level’ parameters
describe the mean and variance in divergence time (τ) and
θ within each simulated multiple taxon-pair data set, while
the ‘lower level’ parameters are the values of τ and θ for each
taxon pair within each simulated data set.
Each simulated data set consisted of 10 taxon pairs that
diverged at time τ, and samples from each sister taxon contained 12 diploid individuals (Fig. 1). For each of the 10 000
data sets simulated under each of the 10 divergence time
hypotheses (Fig. 2), we calculated several comparative
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
phylogeographic summary statistics (Table 1). For eight
out of 10 of these divergence time hypotheses, τ varied
across taxon pairs by drawing it from a particular gamma
distribution that was constrained by a particular mean and
variance of τ (Fig. 2a, b). For the two other divergence time
hypotheses, τ was either drawn from a uniform prior distribution or a mixed gamma distribution with four peaks
corresponding to major events of climate change (Fig. 2c):
the last glacial maximum (20 000 years bp); the previous glacial
maximum (150 000 years bp); the Pliocene–Pleistocene
transition (2 million years ago (Ma)); and the Pliocene–
Miocene boundary (5 Ma).
For each simulated taxon pair, the population mutation
parameter (θ) of the ancestral (θA) and two daughter
populations (θ1 and θ2 at τ = 0) were held equal to each
other while θ1 and θ2 were equally rescaled during the
bottleneck phase (Fig. 1). These parameters (θA, θ1 and θ2)
varied among taxon pairs within each 10 taxon-pair data
set according to a gamma distribution with α = 3.5 and
β = 0.288, approximately corresponding to values of θ that
range between 0.0 and 3.0 (mean of 1.02 and SD = 0.55;
Fig. 3). This gamma distribution describes the range of
θ that is normally found for intron loci and the mean and
variance were specifically estimated from seven intron loci
collected from two taxon pairs of carlia skinks (Dolman
& Phillips 2004; Dolman & Moritz in review) using the
program im (Hey & Nielsen 2004). We explored multiple
taxon-pair divergence models with and without a bottleneck.
In the former case, the demographic expansion parameters
were fixed at NBott1 = 0.5N1, NBott2 = 0.5N1, τBott1 = 0.5τ, and
τBott2 = 0.5τ (Fig. 1; Table 2).
214 M . J . H I C K E R S O N , G . D O L M A N and C . M O R I T Z
Simulation procedure
The overall framework for simulating the single and 10 taxonpair data sets according to a coalescent model used standard
methodology (Hudson 1983, 1990) by drawing parameters
used for each simulated iteration from their respective prior
distributions and subsequently calculating the distributions
of the summary statistics over a set number of iterations.
Specifically, a C program drew the parameters from their
respective prior distributions, and these parameter
values were subsequently used as inputs for Hudson’s
coalescent simulator (Hudson 2002). Subsequently, another
C program generated summary statistics for each simulated
sample, constructed their distributions and statistical powers
(a modified version of Hudson’s sample_stats, 2003). These
three C programs worked in consort by using a Perl script.
The following general procedure was used to generate the
summary statistics under each multiple taxon-pair divergence
hypothesis:
Step 1. Randomly draw NBott1, NBott2, τBott1 and τBott2 for
each data set from corresponding prior distributions or hold at fixed value depending on model.
Step 2. Randomly draw θ for each taxon pair from a gamma
distribution (Fig. 3) and draw τ for each taxon pair
from the prior distribution depicting a particular
vicariance hypothesis (Fig. 2).
Step 3. Using these randomly drawn parameter values,
simulate the independent genealogical histories
with mutations for each locus (400 bp) within each
taxon pair as described in Hudson (1990).
Step 4. Repeat steps two and three for each taxon pair
within a single data set.
Step 5. Compute summary statistics (Table 1) for each 10
taxon-pair data set.
Step 6. Repeat steps one through five 10 000 times for each
divergence time hypothesis (Fig. 2).
Statistical power
We report statistical power for the summary statistics that
were found to best discriminate among near-simultaneous
and variable τ hypotheses. Specifically, we compared the
summary statistics and calculated their respective statistical
powers among pairs of hypotheses. In each comparison,
we compared a near simultaneous τ hypothesis and a
variable τ hypothesis, and always considered the former to
be the null hypotheses. Each null hypothesis, H0 (H0.025A,
H0.25A, H1.25A, H2.5A, and H5.0A), was compared to a respective
alternative hypothesis, HAlt (H0.25B, H0.25B, H1.25B, H2.5B,
Hmixed and Huniform; Fig. 2). Statistical power was defined
as the probability of rejecting the null hypothesis given that
the data were generated by the alternative hypothesis and
an α probability of falsely rejecting this null hypothesis.
The empirical cut-off points for calculating the power of
each summary statistic were obtained by simulating each
summary statistic under the null hypothesis. Because the
distribution of each summary statistic simulated under
the null hypothesis was usually bounded by zero, we chose
our empirical cut-off points to correspond to the upper
5% significance level (one-tailed test). For each test, 10 000
simulations of the data under null hypothesis were compared to 10 000 simulations of the data under the alternative
hypothesis.
Results
Expectation, variance and correlation of summary
statistics
Using among-taxon-pair variance in a summary statistic to
test for variable divergence among taxon pairs can be successful if the summary statistic is correlated with τ (criterion 1).
Given the models with and without a bottleneck, all of
the summary statistics tended to increase with increasing
τ, with the exception of πw and Tajima’s D. The former
remained close to 1.0 and makes it a less suitable summary
statistic for testing multiple taxon-pair hypotheses (criterion
1). Although Tajima’s D initially decreases with increasing
τ, it eventually increases with increasing τ (criterion 1;
Fig. 4). Considering criterion 2, variance in four of the seven
summary statistics (π, πb, πnet, S) greatly increased with
increasing divergence time under both demographic models
(criterion 2; Fig. 4). We chose to only eliminate S, given that
its increase in variance was most severe and that the others
remained useful by strongly satisfying criterion 1.
The correlations between some pairs of summary statistics
were often heavily dependent on τ, while the correlation
of other pairs remained independent of τ (Fig. 5). Among
summary statistics satisfying criteria 1 and 2, π and πb were
heavily correlated at increasing τ, and both became heavily
correlated with πnet with increasing τ (Fig. 5). Because πb was
more strongly correlated with πnet, πb was eliminated from
the subsequent multiple taxon-pair analysis. S, the number
of segregating sites was heavily correlated with π, πb, πnet,
and θW. On the other hand, Tajima’s D, π and θW were never
heavily correlated with each other under either demographic
model, and while all three became correlated with πnet
with older τ, this was to a lesser degree than correlations
involving πb or S (Fig. 5). Overall, Tajima’s D was the least
correlated with any of the other summary statistics.
Based on the three criteria, we selected π, πnet, D, and θW
to explore in comparative phylogeographic models. The
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
P H Y L O G E O G R A P H I C S U M M A R Y S T A T I S T I C S 215
Fig. 4 The expectation and variance of the seven summary statistics (Table 1) calculated from 100 000 single taxon-pair data sets simulated
under a range of divergence times. Single-locus data sets are considered in (a) through (g), and 15 loci data sets are depicted in (h) through
(n). In the later case, the summary statistics are averaged across loci.
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
216 M . J . H I C K E R S O N , G . D O L M A N and C . M O R I T Z
Fig. 5 Correlation coefficients among pairs of summary statistics across a range of τ (0–2.0; 4N generations). Values from each τ are from
100 000 single taxon-pair simulation replicates under a model. Single-locus values are (a) through (d) and the 15 loci values are depicted in
(e) through (h).
results of the simulations were consistent with previous
simulation studies (Simonsen et al. 1995), and previous
derivations of the means and variances for both twopopulation vicariance and panmictic (τ = 0) models
(Takahata & Nei 1985; Hudson et al. 1987; Fu 1995;
Wakeley & Hey 1997; Vasco et al. 2001).
Ten taxon-pair divergence model
Of the 10 comparative phylogeographic summary statistics
we explored (Table 1), six achieved high statistical power
(> 0.5) in testing near-simultaneous divergence given modest
numbers of loci (Table 3). The effect of a demographic
expansion involving a bottleneck subsequent to divergence
only had a slight negative or positive affect on the power
of the summary statistics (Table 3b).
With and without a bottleneck, var(πnet), var(D), and
cov(πnet, D) were the most useful summary statistics,
but their power depended on which hypothesis was
being tested. Specifically, var(πnet) was superior to the other
summary statistics when testing for recent simultaneous
vicariance (H0.025A vs. H0.25B; H0.25A vs. H0.25B). Conversely,
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
P H Y L O G E O G R A P H I C S U M M A R Y S T A T I S T I C S 217
Table 3 Statistical power of comparative phylogeographic summary statistics to reject H0 given HAlt is the true vicariance hypothesis. The
considered vicariance hypotheses are shown on Fig. 1. Statistical power was calculated for 1, 5, 15 and 30 loci, and under a model without
an instantaneous bottleneck (a), and with a 50% reduction in population size during τBott1 and τBott2
(a)
(b)
H0
1 locus
5 loci
15 loci
30 loci
HAlt
H0
1 locus
5 loci
15 loci
30 loci
HAlt
var(πnet)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.90
0.35
0.27
0.16
0.10
0.10
0.95
0.41
0.39
0.20
0.13
0.12
0.98
0.59
0.48
0.21
0.12
0.11
0.99
0.71
0.54
0.28
0.10
0.13
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
var(πnet)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.87
0.23
0.21
0.12
0.10
0.09
0.95
0.34
0.26
0.18
0.11
0.12
0.97
0.60
0.39
0.23
0.10
0.15
0.98
0.67
0.43
0.27
0.14
0.17
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
var(D)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.06
0.12
0.13
0.41
0.42
0.47
0.08
0.16
0.33
0.66
0.72
0.78
0.10
0.23
0.71
0.70
1.00
1.00
0.11
0.28
0.88
0.95
1.00
1.00
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Hmixed
var(D)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.07
0.13
0.17
0.18
0.29
0.34
0.10
0.13
0.25
0.25
0.61
0.67
0.14
0.21
0.55
0.60
0.98
1.00
0.16
0.22
0.77
0.90
1.00
1.00
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(πnet, D)
H0.025A
0.06
H0.25A
0.05
H1.25A
0.29
H2.5A
0.24
H5.0A
0.35
H5.0A
0.39
0.39
0.10
0.44
0.57
0.61
0.64
0.18
0.05
0.75
0.51
0.82
0.85
0.09
0.05
0.92
0.68
0.88
0.93
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(πnet, D)
H0.025A
0.05
H0.25A
0.06
H1.25A
0.25
H2.5A
0.24
H5.0A
0.36
H5.0A
0.41
0.07
0.09
0.29
0.26
0.42
0.48
0.06
0.11
0.34
0.75
0.76
0.82
0.10
0.04
0.78
0.62
0.87
0.92
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(πnet, θW)
H0.025A
0.06
H0.25A
0.05
H1.25A
0.21
H2.5A
0.21
H5.0A
0.05
H5.0A
0.06
0.73
0.24
0.20
0.20
0.10
0.08
0.75
0.26
0.20
0.19
0.08
0.09
0.80
0.25
0.22
0.18
0.06
0.11
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(πnet, θW)
H0.025A
0.56
H0.25A
0.11
H1.25A
0.12
H2.5A
0.08
H5.0A
0.05
H5.0A
0.06
0.78
0.19
0.17
0.13
0.07
0.06
0.78
0.26
0.22
0.14
0.06
0.08
0.77
0.23
0.20
0.17
0.08
0.11
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
var(π)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.06
0.05
0.09
0.10
0.05
0.06
0.16
0.09
0.16
0.13
0.08
0.07
0.18
0.14
0.16
0.12
0.06
0.07
0.18
0.11
0.18
0.18
0.05
0.09
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
var(π)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.08
0.09
0.11
0.12
0.05
0.05
0.13
0.12
0.16
0.15
0.06
0.07
0.15
0.11
0.18
0.15
0.05
0.08
0.17
0.11
0.18
0.18
0.07
0.11
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
var(θW)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.06
0.05
0.09
0.04
0.05
0.06
0.30
0.12
0.12
0.06
0.05
0.05
0.30
0.11
0.10
0.08
0.06
0.05
0.33
0.10
0.13
0.12
0.03
0.07
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
var(θW)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.16
0.08
0.12
0.10
0.05
0.04
0.21
0.10
0.13
0.12
0.06
0.06
0.23
0.10
0.12
0.11
0.04
0.06
0.24
0.10
0.12
0.15
0.06
0.07
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(π, πnet)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.06
0.05
0.29
0.04
0.05
0.05
0.80
0.21
0.26
0.07
0.08
0.07
0.73
0.23
0.28
0.15
0.09
0.08
0.79
0.24
0.31
0.22
0.06
0.12
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(π, πnet)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.61
0.13
0.16
0.07
0.06
0.06
0.79
0.16
0.22
0.16
0.07
0.06
0.77
0.22
0.27
0.19
0.07
0.11
0.76
0.21
0.26
0.21
0.09
0.13
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
218 M . J . H I C K E R S O N , G . D O L M A N and C . M O R I T Z
Table 3 Continued
(a)
(b)
H0
1 locus
5 loci
15 loci
30 loci
HAlt
H0
1 locus
5 loci
15 loci
30 loci
HAlt
cov(π, D)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.06
0.05
0.29
0.24
0.35
0.39
0.05
0.10
0.29
0.32
0.53
0.58
0.04
0.14
0.45
0.37
0.58
0.64
0.04
0.14
0.55
0.46
0.61
0.72
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(π, D)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.06
0.05
0.16
0.15
0.27
0.28
0.08
0.12
0.23
0.25
0.34
0.37
0.07
0.14
0.43
0.38
0.55
0.61
0.05
0.16
0.51
0.49
0.65
0.76
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(D, θW)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.06
0.05
0.29
0.24
0.35
0.37
0.06
0.09
0.23
0.23
0.42
0.46
0.04
0.09
0.13
0.24
0.45
0.49
0.03
0.10
0.41
0.37
0.48
0.55
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(D, θW)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.06
0.08
0.13
0.16
0.22
0.20
0.07
0.10
0.20
0.23
0.34
0.36
0.06
0.11
0.34
0.29
0.46
0.49
0.05
0.12
0.39
0.36
0.53
0.57
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(π, θW)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.06
0.05
0.09
0.04
0.05
0.05
0.26
0.09
0.13
0.04
0.08
0.08
0.23
0.12
0.13
0.09
0.06
0.08
0.25
0.10
0.16
0.15
0.04
0.10
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
cov(π, θW)
H0.025A
H0.25A
H1.25A
H2.5A
H5.0A
H5.0A
0.11
0.09
0.09
0.06
0.07
0.06
0.16
0.11
0.15
0.12
0.06
0.06
0.18
0.11
0.03
0.14
0.04
0.05
0.20
0.11
0.13
0.16
0.07
0.09
H0.25B
H0.25B
H1.25B
H2.5B
Hmixed
Huniform
the power of var(D) was superior when testing more
ancient simultaneous vicariance hypotheses (H2.5A vs.
H2.5B; H5.0A vs. Hmixed; H5.0A vs. Huniform; Table 3), and
cov(πnet, D) achieved the highest power when testing
hypotheses involving moderate divergence times (H1.25A
vs. H1.25B; Table 3).
Discussion
Comparative phylogeographic inference
Inferring the temporal distribution of vicariance across
codistributed taxon pairs has been a vexing problem for
biogeographers (Darwin 1859; MacArthur & Wilson 1967;
Case 1983; Brown 1995; Avise 2000). While molecular phylogeography provides hope in this endeavour (Avise 2000),
two problematic issues that are informed from theoretical
population genetics illustrate the intrinsic difficulty in solving
this riddle of comparative phylogeography (Edwards &
Beerli 2000; Arbogast et al. 2002).
The first problematic issue is that intrinsic coalescent and
mutation variance will result in variable genetic divergences
across taxon pairs under most situations (Arbogast et al.
2002), even if taxon pairs are identical in all characteristics.
This is expected to be found when using a single locus such
as mitochondrial DNA because each mitochondrial tree
is but a single realization of a highly variable process,
such that biased inferences easily arise without statistically
incorporating this inherent variance (Nichols 2001; Knowles
& Maddison 2002; Hudson & Turelli 2003). This problematic
issue is most clearly illustrated in the ‘natural experiment’
of the Panamanian Isthmus splitting marine taxa into sister
taxon pairs approximately 3.1 Ma (Jordan 1908; Coates et al.
1992). The variation in mitochondrial divergences across
sister taxon pairs might first appear to signify variation in
divergence times (Lessios et al. 2001; Marko 2002), yet such
patterns are expected under both simultaneous and variable
vicariance histories due to these two sources of intrinsic
variance that become most apparent in single-locus data
sets (Hickerson et al. 2003).
Despite the steady stream of cautionary reminders about
the hazards of basing phylogeographic inference on a single
locus (Takahata 1989; Moore 1995; Hoelzer 1997; Maddison
1997; Bermingham & Moritz 1998; Kuhner et al. 1998;
Edwards & Beerli 2000; Beerli & Felsenstein 2001; Hare &
Palumbi 2001; Hudson & Turelli 2003; Ballard & Whitlock
2004), the high cost of developing nuclear intron markers
in a broad range of ‘nonmodel’ taxa have so far prevented
widespread use of introns or other independently segregating sets of linked SNPs. Assuming that future advances
will allow nuclear loci to be more routinely collected, there
should be guidance in how many intron loci are sufficient
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
P H Y L O G E O G R A P H I C S U M M A R Y S T A T I S T I C S 219
for sound inference across a range of phylogeographic
questions (Edwards & Beerli 2000; Hare & Palumbi 2001;
Zhang & Hewitt 2003; Aitken et al. 2004), and the results
of this study demonstrate that previously intractable problems in phylogeography can be solved with reasonable
numbers of loci.
The second problematic issue arises from amongtaxon-pairs variability in the parameters that affect genetic
divergences other than the actual timings of vicariance.
This can include differences in among-taxon-pair mutation
rates, ancestral population sizes, postdivergence migration
rates (admixture), degrees of subdivision, and/or bottleneck
magnitudes. Again, the Panama Isthmus example illustrates
this difficulty in that the observed variability in single-locus
genetic divergences across taxon pairs could have arisen
from among-taxa differences in any of these confounding
parameters. This second issue is daunting, but there is
hope in tackling it by identifying the simplest underlying
population genetic model based on a priori biological and/
or nonbiological hypotheses (Wakeley 2004), and incorporating among-taxa variability in these parameters directly
into the analysis via a prior distribution. It has been suggested that ABC approaches are well suited in this endeavour
(Beaumont & Rannala 2004). Our primary objective here is
to identify a pool of summary statistics that can extract the
important features of phylogeographic data sets that are
relevant to testing comparative phylogeographic hypotheses within a future simulation-based framework such
as ABC.
Summary statistics for comparative phylogeographic
inference
Our initial single taxon-pair simulations identify π, πnet, θW,
and Tajima’s D to be a potentially useful set of minimally
correlated summary statistics that contain useful information
regarding simultaneous vicariance, with Tajima’s D being
the least correlated with the other summary statistics (Figs 4
and 5). By using statistical power to gauge the suitability of
a particular summary statistic, our results indicate that var(D),
var(πnet), cov(πnet, D), cov(π, πnet), cov(π, D), and cov(πnet, θW)
are useful measures for testing simultaneous vicariance.
However, the power of these greatly depended on which
hypothesis was being tested. When testing hypotheses
of more recent divergence times (i.e. H0.025A, H0.25B, H0.25A),
var(πnet) achieved the highest statistical power whereas
var(D) was superior when testing older divergence time
hypotheses (i.e. H1.25A, H1.25B, H2.5A, H2.5B, H5.0A, Hmixed,
Huniform; Table 3). This could be counter-intuitive because
πnet is normally used to estimate divergence time (Nei & Li
1979) whereas significantly negative values of Tajima’s
D are often used to detect selective sweeps or population
growth (Tajima 1989). However, the latter has a second
purpose in being able to detect elevated balancing selection
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
or subdivision from significantly positive values. The superior
power of Tajima’s D at older near-simultaneous divergence
times becomes clear with closer examination of our initial
single taxon-pair simulations (Fig. 4) as well as previous
theoretical studies (Takahata & Nei 1985; Hudson et al.
1987; Tajima 1989; Fu 1995; Wakeley & Hey 1997; Vasco
et al. 2001; Pluzhnikov et al. 2002).
In our initial single taxon-pair simulations and consistent
with previous studies, πnet increases with increasing τ (Fig. 4),
and the greater accumulation of fixed differences between
diverged populations leads Tajima’s D to eventually increase
with greater τ (Takahata & Nei 1985; Hudson et al. 1987;
Simonsen et al. 1995; Fig. 4). Also consistent with previous
studies (Takahata & Nei 1985; Hudson et al. 1987; Tajima
1989), the per-taxon-pair variance of πnet becomes greatly
inflated with increasing τ (Fig. 4a), whereas the per-taxon-pair
variance of Tajima’s D is stable and extremely low in comparison (< 1.0; Fig. 4b). Therefore correctly rejecting older
simultaneous vicariance histories should become difficult
with var(πnet) because this test statistic becomes inflated
across taxon pairs regardless of whether τ was nearly
simultaneous (H5.0A) or not (Hmixed). Even collecting more
loci does not markedly erase this problem for var(πnet), in
which the variance of πnet approaches 0.3 at the highest τ
given 15 loci (Fig. 4h), whereas the variance of Tajima’s
D is approximately 0.05 throughout all τ given 15 loci
(Fig. 4i).
Although we specifically consider the variance of a summary statistic (or covariance of pairs of summary statistics)
across taxon pairs as a single test statistic for testing a
comparative vicariance hypothesis, an ABC framework
can use more information from the data by simultaneously
using multiple summary statistics to test such hypotheses
and estimate parameters (Estoup et al. 2004). Our simulation study suggests that such an ABC method should
consider π, Tajima’s D, πnet, and θW from each taxon pair as
separate summary statistics, and especially Tajima’s D
because it was found to be relatively uncorrelated with the
other summary statistics across divergence time (Fig. 5). In
practice such a pool will likely be reduced because D and
πnet are in fact composite summary statistics. In this case,
we can consider their components as summary statistics,
and again use these values from each taxon pair as separate
summary statistics instead of the overall variance. For
example, instead of using var(πnet), we could use each
within taxon average pairwise difference (πw) and average pairwise differences between each sister taxon (πb).
Likewise, instead of using Tajima’s D, the summary
statistic that was most uncorrelated with the other summary
statistics, we can separately use its components, π, θW and
var(π – θW) from each taxon pair as summary statistics
(Tajima 1989). In this case, a data set of i taxon pairs would
yield a pool of summary statistics that include π1 … πi, πw1
… πwi, πb1 … πbi, θW1 … θWi, and var(π – θW)1 … var(π – θW)i.
220 M . J . H I C K E R S O N , G . D O L M A N and C . M O R I T Z
Power and loci
Planning a phylogeographic study involves balancing the
costs of an optimized sampling strategy with the resulting
gains in statistical power for testing competing hypotheses.
In such studies, increasing sample size is achieved by collecting data from more unlinked loci, base pairs, individuals and/
or locations. In general, increasing sample size will reduce
the variance in parameter estimates used to test hypotheses,
yet these different strategies for increasing sample size have
different statistical gains and drastically different monetary
and temporal costs. For instance, collecting additional intron
loci can be difficult given the obstacles of resolving phase
and the difficulty in using ‘universal primers’ that are
workable in a variety of taxa (Hare & Palumbi 2001; Zhang
& Hewitt 2003; Aitken et al. 2004). It is then imperative
to assess the gains in statistical power resulting from
these various strategies for increasing ‘sample size’ before
embarking on such a study. Although the resulting gains
in power from collecting more base pairs or individuals
are somewhat straightforward (Tajima 1983; Pluzhnikov &
Donnelly 1996), determining how many unlinked nuclear
loci are required for reasonable power in comparative
phylogeographic studies is less obvious.
According to the properties of sample means, collecting
additional loci should lower the variance in a summary
statistic and this decrease in variance should be proportional
to how many loci are collected. In the case of a summary
statistic such as Tajima’s D, collecting additional loci with
equal mutation rates will result in var(D) = var(D)/l, where
l is the number of loci (DeGroot 1986). This is largely manifest
in our initial single taxon-pair simulations in which the
variance of Tajima’s D is 0.92 with a divergence time of
zero (τ = 0) and a single locus and 0.0612 with τ = 0 and 15
loci collected (Fig. 4).
Under the multiple taxon-pair histories, uniformity in
divergence times and other key parameters across taxon
pairs will result in a further reduction in the variance of
Tajima’s D with more loci because the variance in D will be
var(D)/lT, where T is number of taxa and l is the number
of loci. Therefore the variable-τ history should consistently
inflate var(D) when collecting more loci given the effect
that τ has on D averaged across loci demonstrated in
our initial single taxon-pair simulations (Fig. 4). In this
case var(D) should be consistently inflated to the extent to
which τ varies among taxa. It is encouraging that a single
metric like var(D) can successfully test simultaneous vicariance hypotheses with a moderate number of loci. Using
the components of var(D) simultaneously with the components of var(πnet) within a future ABC framework is likely
to make testing simultaneous vicariance tractable given
this reasonable number of loci and the range of parameter
conditions we explored, instead of the nearly intractable
problem presented by Edwards & Beerli (2000).
Edwards and Beerli proposed lτ/θ > 1 as a criterion for
determining the number of loci required to reject τ = 0 in a
single taxon pair. Although it is a different hypothesis test,
the power of var(πnet) to reject H0.025A given that H0.25B was
the true history across 10 taxon pairs was > 0.9 given 5 loci,
as opposed to the ∼16.6 loci required to reject τ = 0 at a single taxon pair according to their criterion (Table 3a). For
many other scenarios, statistical power was > 0.5 with only
5–10 nuclear loci, an amount of data that can be feasibly
collected in many laboratories, especially with the increasing phylogenetic breadth of genomic resources and development of efficient assays. While this does not conflict with
the single taxon-pair criterion proposed by Edwards and
Beerli, our success in being able to correctly reject simultaneous τ across 10 taxon pairs given among-taxon-pair variation in θ is in contrast to their pessimism regarding this
difficult ‘data-hungry’ problem (Edwards & Beerli 2000).
Comparative phylogeographic complexity
It is sobering to note that some conditions will make testing
simultaneous vicariance extremely difficult and will indeed
make it a ‘data-hungry’ problem without having good prior
information about how parameters vary across taxon pairs
(Edwards & Beerli 2000). According to our simulations that
incorporated post-divergence migration (results not shown),
and previous theoretical work (Wakeley 1996; Nielsen &
Slatkin 2000; Kalinowski 2002), migration after divergence
will obscure the ability to distinguish among histories because
it tends to erase the signal of genetic divergence between
populations. Variance in demographic expansion could also
hinder testing simultaneous vicariance. Although we found
that a simple demographic expansion (Fig. 1) and a range
of such demographic expansions after vicariance (results
not shown) did not greatly hinder testing simultaneous
vicariance, variance in demographic expansion across taxon
pairs could exacerbate testing simultaneous vicariance
by causing an elevation in the variance of Tajima’s D under
both simultaneous and variable divergence time histories
(Simonsen et al. 1995). Furthermore, although we allowed
θ to vary across taxon pairs, we did not explore variation
in µ across loci, a factor that might greatly complicate such
hypothesis testing. This reminds us that comparative
phylogeographic studies will be more tractable in groups
of taxa having low dispersal potential across the barrier
leading to vicariance and when using loci for which the
distribution of mutation rates across taxa or loci can be
independently estimated.
Fortunately, an important advantage of simulation-based
frameworks is that arbitrary complexity can be easily built
into the underlying model. One can initially use simple
models to identify processes that violate the simple model’s
assumptions. Subsequently, one can easily expand the
simulation model to incorporate sufficient biological realism
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
P H Y L O G E O G R A P H I C S U M M A R Y S T A T I S T I C S 221
and complexity that is guided by a priori hypotheses and
independent estimates (Tavaré et al. 1997; Beaumont et al.
2002; Estoup et al. 2004). For example, independent estimates
of variability in mutation rates can be directly incorporated
by using a gamma-distributed prior distribution for µ.
Alternatively, this flexibility allows one to incorporate
uncertainty in across-loci variation in µ by using uninformative priors for the two free parameters of a gamma
distribution (α and β). Likewise, uncertainty regarding
variation in θ and demographic expansion parameters
that vary across taxon pairs can be built into the model.
Additionally, selection at certain loci can be detected and
incorporated into a simulation-based analysis by hierarchical
Bayesian methods or outlier tests (Lewontin & Krakauer
1973; Galtier et al. 2000; Storz & Beaumont 2002; Luikart
et al. 2003; Beaumont 2004; Hey & Nielsen 2004). Although
we did not report results incorporating recombination, we
found that recombination only served to increase statistical
power by decoupling linked polymorphisms and thereby
reducing the variance (results not shown; Wakeley & Hey
1997).
Another consideration is that our model does not explicitly
incorporate subdivision, a parameter that can strongly
influence the patterns of the coalescent (Arbogast et al.
2002; Rosenberg & Feldman 2002). However, our coalescent model may still be justified if θ is rescaled by the
number of demes and degree of subdivision, a reasonable
assumption across various subdivision models (Wakeley
2000, 2004; Wakeley & Aliacar 2001; Nordborg & Krone
2002). Although the model we consider is not spatial, the
general framework can be designed for geographically
explicit models, such as comparative phylogeographic
dispersal histories (Estoup et al. 2004) and ecologically
deterministic distributional histories (Ravelo et al. 2004).
In this case, the parameters underlying the biogeographic
hypotheses that are based on ecological and palaeoclimatic
models (Hugall et al. 2002) can be directly incorporated
into the simulation model as parameters underlying the
comparative phylogeographic vicariance hypotheses
(Fig. 2).
Conclusion
We found that the power of a particular summary statistic
used alone to test for simultaneous vicariance depended
on which particular hypothesis was being tested. Using the
summary statistics π, πw, πb, θW and var(π – θW)1 from each
taxon pair simultaneously in an ABC framework should
improve upon the statistical powers we report in this
study, and therefore we are currently developing such a
framework for comparative phylogeographic inference.
Although we did not consider every summary statistic
under the sun, we did investigate the commonly used ones
that are known to capture the relevant signals underlying
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
comparative phylogeographic data sets with regards to
demography and population divergence.
Acknowledgements
We thank S. Baird, M. Slatkin, R. Young, X. Zhao, F. Rousset and
the anonymous reviewers for advice on improving this study. We
thank J. Mackenzie for assisting us with the AWT data. We greatly
thank E. Stahl, N. Takebayashi, K. Thornton, J. Novembre, and
E. Anderson for assistance and advice regarding the simulations.
Support for M. J. Hickerson was provided by a National Science
Foundation postdoctoral grant in interdisciplinary informatics.
The Perl and C code routines used for the simulations are available
from M. Hickerson upon request.
References
Aitken N, Smith S, Schwartz C, Morin PA (2004) Single nucleotide
polymorphism (SNP) discovery in mammals: a targeted-gene
approach. Molecular Ecology, 13, 1423–1431.
Arbogast BS, Edwards SV, Wakeley J, Beerli P, Slowinski JB (2002)
Estimating divergence times from molecular data on phylogenetic
and population genetic timescales. Annual Review of Ecology and
Systematics, 33, 707–740.
Avise JC (2000) Phylogeography: The History and Formation of Species.
Harvard University Press, Cambridge, Massachusetts.
Avise JC, Walker D, Johns GC (1998) Speciation durations and
Pleistocene effects on vertebrate phylogeography. Proceedings of
the Royal Society of London. Series B, Biological Sciences, 265, 1707–
1712.
Bahlo M, Griffiths RC (2000) Inference from gene trees in a subdivided
population. Theoretical Population Biology, 57, 79–95.
Ballard JWO, Whitlock MC (2004) The incomplete natural history
of mitochondria. Molecular Ecology, 13, 729–743.
Beaumont BA (2004) Recent developments in genetic data analysis:
what can they tell us about human demographic history? Heredity,
92, 365–379.
Beaumont BA, Rannala B (2004) The Bayesian revolution in genetics.
Nature Reviews Genetics, 5, 251–261.
Beaumont MA, Zhang W, Balding DJ (2002) Approximate
Bayesian computation in population genetics. Genetics, 162,
2025–2035.
Beerli P, Felsenstein J (2001) Maximum likelihood estimation
of a migration matrix and effective population sizes in n
subpopulations by using a coalescent approach. Proceedings of
the National Academy of Sciences, USA, 98, 4563–4568.
Bermingham E, Moritz C (1998) Comparative phylogeography:
concepts and applications. Molecular Ecology, 7, 367–369.
Brown JH (1995) Macroecology. University of Chicago Press, Chicago.
Case TJ (1983) Sympatry and size similarity in Cnemidophorus. In:
Lizard Ecology: Studies of a Model Organism (eds Huey RB, Pianka ER,
Schoener TW), pp. 297–325. Harvard University Press, Cambridge,
Massachusetts.
Coates AG, Jackson JBC, Collins LS et al. (1992) Closure of the
Isthmus of Panama: the near-shore marine record of Costa
Rica and western Panama. Geological Society of America Bulletin,
104, 814–828.
Darwin C (1859) The Origin of Species. John Murray, London.
DeGroot MH (1986) Probability and Statistics. Addison-Wesley,
Reading, Massachusetts.
222 M . J . H I C K E R S O N , G . D O L M A N and C . M O R I T Z
Dolman G, Moritz C (in review) Demography of diversification of
carlia skinks from Australian tropical rainforest: inference from
multi-locus coalescent analyses.
Dolman G, Phillips B (2004) Single-copy nuclear DNA markers
characterized for comparative phylogeography in Australian
wet tropics rainforest skinks. Molecular Ecology Notes, 4, 185 –
187.
Edwards SV, Beerli P (2000) Perspective: gene divergence, population divergence, and the variance in coalescence time in
phylogeographic studies. Evolution, 54, 1839 –1854.
Estoup A, Wilson IJ, Sullivan CJ-MC, Moritz C (2001) Inferring
population history from microsatellite and enzyme data in serially
introduced cane toads, Bufo marinus. Genetics, 159, 1671–1687.
Estoup A, Beaumont BA, Sennedot F, Moritz C, Cornuet J-M
(2004) Genetic analysis of complex demographic scenarios:
spatially expanding populations of the cane toad, Bufo marinus.
Evolution, 58, 2021–2036.
Excoffier L, Novembre J, Schneider S (2000) simcoal: a general
coalescent program for the simulation of molecular data in
interconnected populations with arbitrary demography. Journal
of Heredity, 91, 506 – 509.
Excoffier L, Estoup A, Cornuet J-M (2005) Bayesian analysis
of an admixture model with mutations and arbitrarily linked
markers. Genetics, 169, 1727–1738.
Fu Y-X (1995) Statistical properties of segregating sites. Theoretical
Population Biology, 48, 172–197.
Fu Y-X, Li W-H (1993) Statistical tests of neutrality of mutations.
Genetics, 133, 693–709.
Galtier N, Depaulis F, Barton NH (2000) Detecting bottlenecks and
selective sweeps from DNA sequence polymorphism. Genetics,
2, 981–987.
Hare MP, Palumbi SR (2001) Prospects for nuclear gene phylogeography. Trends in Ecology & Evolution, 16, 700 –706.
Hey J, Nielsen R (2004) Multilocus methods for estimating population sizes, migration rates and divergence time, with applications
to the divergence of Drosophila pseudoobscura and D. persimilis.
Genetics, 167, 747–760.
Hickerson MJ, Cunningham CW (2005) Contrasting Quaternary
histories in an ecologically divergent pair of low-dispersing
intertidal fish (Xiphister) revealed by multi-locus DNA analysis.
Evolution, 59, 344– 360.
Hickerson MJ, Gilchrist MA, Takebayashi N (2003) Calibrating
a molecular clock from phylogeographic data: moments and
likelihood estimators. Evolution, 57, 2216 –2225.
Hoelzer GA (1997) Inferring phylogenies from mtDNA variation:
mitochondrial-gene trees versus nuclear-gene trees revisited.
Evolution, 51, 622– 626.
Hudson RR (1983) Properties of a neutral model with intragenic
recombination. Theoretical Population Biology, 23, 183 –201.
Hudson RR (1990) Gene genealogies and the coalescent process.
In: Oxford Surveys in Evolutionary Biology (eds Futuyma D,
Antonovics J), pp. 1– 44. Oxford University Press, Oxford.
Hudson RR (2002) ms – a program for generating samples under
neutral models. Bioinformatics, 18, 337–338.
Hudson RR, Turelli M (2003) Stochasticity overrules the ‘threetimes rule’: genetic drift, genetic draft, and coalescence times for
nuclear loci versus mitochondrial DNA. Evolution, 57, 182–190.
Hudson RR, Kreitman M, Aguade M (1987) A test of neutral
molecular evolution. Genetics, 116, 153 –159.
Hugall A, Moritz C, Moussalli A, Stanisic J (2002) Reconciling
paleodistribution models and comparative phylogeography in
the Wet Tropics rainforest land snail Gnarosophia bellendenkerensis
(Brazier 1875). Proceedings of the National Academy of Sciences,
USA, 99, 6112–6117.
Johns GC, Avise JC (1998) A comparative summary of genetic
distances in the vertebrates from the mitochondrial cytochrome
b gene. Molecular Biology and Evolution, 15, 1481–1490.
Johnson NK, Cicero C (2004) new mitochondrial DNA data affirm
the importance of Pleistocene speciation in North American
Birds. Evolution, 58, 1122–1130.
Jordan DS (1908) The law of geminate species. American Naturalist,
42, 73–80.
Kalinowski ST (2002) Evolutionary and statistical properties of
three genetic distances. Molecular Ecology, 11, 1263–1273.
Knowles LL, Maddison WP (2002) Statistical phylogeography.
Molecular Ecology, 11, 2623–2635.
Knowlton N, Weigt LA (1998) New dates and new rates for divergence across the Isthmus of Panama. Proceedings of the Royal
Society of London. Series B, Biological Sciences, 265, 2257–2263.
Kuhner MK, Yamato J, Felsenstein J (1998) Maximum likelihood
estimation of population growth rates based on the coalescent.
Genetics, 149, 429–434.
Lessios HA, Kessing BD, Pearse JS (2001) Population structure and
speciation in tropical seas: global phylogeography of the sea
urchin Diadema. Evolution, 55, 955–975.
Lewontin RC, Krakauer JK (1973) Distribution of gene frequency
as a test of the theory of the selective neutrality of polymorphisms. Genetics, 74, 175–195.
Luikart G, England PR, Tallman D, Jordan S, Taberlet P (2003) The
power and promise of population genomics: from genotyping
to genome typing. Nature Reviews Genetics, 4, 981–994.
MacArthur RH, Wilson EO (1967) Theory of Island Biogeography.
Princeton University Press, Princeton, New Jersey.
Maddison WP (1997) Gene trees in species trees. Systematic Biology,
46, 523–536.
Marko PB (2002) Fossil calibration of molecular clocks and the
divergence times of geminate species pairs separated by the
Isthmus of Panama. Molecular Biology and Evolution, 19, 2005 –
2021.
Moore WS (1995) Inferring phylogenies from mtDNA variation:
mitochondrial-gene trees versus nuclear-gene trees. Evolution,
49, 718–726.
Nei M, Li W (1979) Mathematical model for studying variation in
terms of restriction endonucleases. Proceedings of the National
Academy of Sciences, USA, 76, 5269–5273.
Nelson G, Platnick NI (1981) Systematics and Biogeography:
Cladistics and Vicariance. Columbia University Press, New York.
Nichols R (2001) Gene trees and species trees are not the same.
Trends in Ecology & Evolution, 16, 358–364.
Nielsen R, Slatkin M (2000) Likelihood analysis of ongoing gene
flow and historical association. Evolution, 54, 44–50.
Nielsen R, Wakeley J (2001) Distinguishing migration from
isolation: a Markov chain Monte Carlo approach. Genetics, 158,
885–896.
Nordborg M, Krone SM (2002) Separation of time scales and convergence to the coalescent in structured populations. In: Modern
Developments in Theoretical Population Genetics (eds Slatkin M,
Veuille M), pp. 130–164. Oxford University Press, Oxford.
Plagnol V, Tavare S (2002) Approximate Bayesian computation
and MCMC. In: Monte Carlo and Quasi-Monte Carlo Methods (ed.
Neiderreiter H), pp. 99–114. Springer-Verlag, Berlin.
Pluzhnikov A, Donnelly P (1996) Optimal sequencing strategies
for surveying molecular genetic diversity. Genetics, 144, 1247–
1262.
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
P H Y L O G E O G R A P H I C S U M M A R Y S T A T I S T I C S 223
Pluzhnikov A, Di Rienzo A, Hudson RR (2002) Inferences about
human demography based on multilocus analyses of noncoding
sequences. Genetics, 161, 1209 –1218.
Pritchard JK, Seielstad MTAP-L, Feldman MW (1999) Population
growth of human Y chromosomes: a study of Y chromosome
microsatellites. Molecular Biology and Evolution, 16, 1791–1798.
Ravelo AC, Andreasen DH, Lyle M, Lyle AO, Wara MW (2004)
Regional climate shifts caused by gradual global cooling in the
Pliocene epoch. Nature, 429, 263 –267.
Ricklefs RE, Schluter D (1993) Species diversity: regional and
historical influences. In: Species Diversity in Ecological Communities
(eds Ricklefs RE, Schluter D), pp. 350–363. University of Chicago
Press, Chicago.
Riddle BR, Hafner DJ, Alexander LF, Jaeger JR (2000) Cryptic
vicariance in the historical assembly of a Baja California Peninsular Desert biota. Proceedings of the National Academy of Sciences,
USA, 97, 14438–14443.
Rosenberg NA, Feldman MW (2002) The relationship between
coalescence times and population divergence times. In: Modern
Developments in Theoretical Population Genetics (eds Slatkin M,
Veuille M), pp. 130–164. Oxford University Press, Oxford.
Schneider CJ, Cunningham M, Moritz C (1998) Comparative
phylogeography and the history of endemic vertebrates in the
Wet Tropics rainforests of Australia. Molecular Ecology, 7, 487–
498.
Simonsen KL, Churchill GA, Aquadro CF (1995) Properties of
statistical tests of neutrality for DNA polymorphism data. Genetics,
141, 413–429.
Storz JF, Beaumont BA (2002) Testing for genetic evidence of population expansion and contraction: an empirical analysis of
microsattelite DNA variation using a hierarchical Bayesian model.
Evolution, 56, 154–166.
Tajima F (1983) Evolutionary relationship of DNA sequences in
finite populations. Genetics, 105, 437– 460.
Tajima F (1989) Statistical method for testing the neutral mutation hypothesis by DNA polymorphism. Genetics, 123, 585 –
595.
Takahata N (1989) Gene genealogy in three related populations —
consistency probability between gene and population trees.
Genetics, 122, 957–966.
Takahata N, Nei M (1985) Gene genealogy and variance of
intrapopulational nucleotide differences. Genetics, 110, 325–
344.
© 2006 Blackwell Publishing Ltd, Molecular Ecology, 15, 209–223
Tallmon DA, Luikart G, Beaumont BA (2004) Comparative
evaluation of a new effective population size estimator based on
approximate Bayesian computation. Genetics, 167, 977–988.
Tavaré S, Balding DJ, Griffiths RC, Donnelly P (1997) Inferring
coalescence times from DNA sequence data. Genetics, 145, 505 –
518.
Vasco DA, Crandall KA, Fu Y-X (2001) Molecular population
genetics: coalescent methods based on summary statistics.
In: Computational and Evolutionary Analysis of HIV Molecular
Sequences (eds Rodrigo AG, Learn GH Jr). Kluwer Academic
Publishers, Dordrecht, The Netherlands.
Wakeley J (1996) Distinguishing migration from isolation using
the variance of pairwise differences. Theoretical Population Biology,
49, 369–386.
Wakeley J (2000) The effects of subdivision on the genetic divergence of populations and species. Evolution, 4, 1092–1101.
Wakeley J (2004) Recent trends in population genetics: More data!
More math! Simple models? Journal of Heredity, 95, 397–405.
Wakeley J, Aliacar N (2001) Gene genealogies in a metapopulation. Genetics, 159, 893–905.
Wakeley J, Hey J (1997) Estimating ancestral population parameters.
Genetics, 145, 847–855.
Watterson GA (1975) On the number of segregating sites in genetic
models without recombination. Theoretical Population Biology, 7,
256–276.
Weiss G, von Haeseler A (1998) Inference of population history
using a likelihood approach. Genetics, 149, 1539–1546.
Zhang D, Hewitt GM (2003) Nuclear DNA analyses in genetic
studies of populations: practice, problems and prospects. Molecular
Ecology, 12, 563–584.
M. Hickerson uses multi-locus DNA sequence data to study the
biogeographic history of rocky intertidal fishes and additionally
develops analytical methods for testing comparative phylogeographic hypotheses. As part of her PhD research, G. Dolman
uses multi-locus DNA sequence data to study speciation and
diversification processes in tropical rainforest fauna. C. Moritz is
director of the museum of vertebrate zoology at the University of
California, Berkeley, and his research program combines phylogeographic data with other historical and/or current distributional
data to infer population processes in space and time.